# Applications of the Euler characteristic in bifurcation theory.

Publicacions Matemàtiques (1991)

- Volume: 35, Issue: 2, page 527-535
- ISSN: 0214-1493

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topRybicki, Slawomir. "Applications of the Euler characteristic in bifurcation theory.." Publicacions Matemàtiques 35.2 (1991): 527-535. <http://eudml.org/doc/41711>.

@article{Rybicki1991,

abstract = {Let f: Rn x Rn → Rn be a continuous map such that f(0,λ) = 0 for all λ ∈ Rk. In this article we formulate, in terms of the Euler characteristic of algebraic sets, sufficient conditions for the existence of bifurcation points of the equation f(x,λ) = 0. Moreover we apply these results in bifurcation theory to ordinary differential equations. It is worth to point out that in the last paragraph we show how to verify, by computer, the assumptions of the theorems of this paper.},

author = {Rybicki, Slawomir},

journal = {Publicacions Matemàtiques},

keywords = {bifurcation point; Euler characteristic; Brouwer equations; topological degree},

language = {eng},

number = {2},

pages = {527-535},

title = {Applications of the Euler characteristic in bifurcation theory.},

url = {http://eudml.org/doc/41711},

volume = {35},

year = {1991},

}

TY - JOUR

AU - Rybicki, Slawomir

TI - Applications of the Euler characteristic in bifurcation theory.

JO - Publicacions Matemàtiques

PY - 1991

VL - 35

IS - 2

SP - 527

EP - 535

AB - Let f: Rn x Rn → Rn be a continuous map such that f(0,λ) = 0 for all λ ∈ Rk. In this article we formulate, in terms of the Euler characteristic of algebraic sets, sufficient conditions for the existence of bifurcation points of the equation f(x,λ) = 0. Moreover we apply these results in bifurcation theory to ordinary differential equations. It is worth to point out that in the last paragraph we show how to verify, by computer, the assumptions of the theorems of this paper.

LA - eng

KW - bifurcation point; Euler characteristic; Brouwer equations; topological degree

UR - http://eudml.org/doc/41711

ER -